Rebecca Goldin Ph.D
According to USA Today, “Fractions should be scrapped” – and the whole world seems to be cheering the potential demise of perhaps the most frustrating and demanding topic in elementary school arithmetic. As the paper reported:
A few years ago, Dennis DeTurck, an award-winning professor of mathematics at the University of Pennsylvania, stood at an outdoor podium on campus and proclaimed, “Down with fractions!”
“Fractions have had their day, being useful for by-hand calculation,” DeTurck said as part of a 60-second lecture series. “But in this digital age, they’re as obsolete as Roman numerals are.”
But before the shouts of joy rise to the power of deafening, take a closer look: No one is actually proposing that the idea of fractions be scrapped; Dr. DeTurck was expressing the opinion that decimal expressions are more relevant and important in the age of computers than ratios such as 3/4.
The point is that every fraction (a ratio of two integers) can be expressed as a decimal expression (allowing for infinitely repeating sequences), and vice versa. So fractions and decimals are two different ways of talking about the same nubmers: rational numbers. Irrational numbers, such as the square root of two or the infamous pi, cannot be expressed as a ratio nor as a decimal, though they can be approximated by them (e.g. pi is close to 3.14).
While DeTurck engages mathematicians and math educators over whether the techniques involving ratios are more or less important than the techniques using decimals, no one is questioning the importance of generalizing from integers to fractions, a fundamental concept which is typically a major component of fourth grade mathematics.
(Editor’s note, Rebecca Goldin is an award-winning mathematician at George Mason University)